{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:I4CHVVJZYTALF5KBXFH7UUSSML","short_pith_number":"pith:I4CHVVJZ","canonical_record":{"source":{"id":"1806.00982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-04T06:53:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"93ad8b867a765c92c898396d0e317959a725dc81cecc3640527fad8c6ab30750","abstract_canon_sha256":"8ea0e0d4cbe64ea42eedf0e606dcfd1c3a8bef45263c7410e5e51c8fb6e7ef1c"},"schema_version":"1.0"},"canonical_sha256":"47047ad539c4c0b2f541b94ffa525262c268353038b3daddca81c3c04ca7e406","source":{"kind":"arxiv","id":"1806.00982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00982","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00982v1","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00982","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"I4CHVVJZYTAL","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I4CHVVJZYTALF5KB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I4CHVVJZ","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:I4CHVVJZYTALF5KBXFH7UUSSML","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00982","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-04T06:53:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"93ad8b867a765c92c898396d0e317959a725dc81cecc3640527fad8c6ab30750","abstract_canon_sha256":"8ea0e0d4cbe64ea42eedf0e606dcfd1c3a8bef45263c7410e5e51c8fb6e7ef1c"},"schema_version":"1.0"},"canonical_sha256":"47047ad539c4c0b2f541b94ffa525262c268353038b3daddca81c3c04ca7e406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:43.310994Z","signature_b64":"hhEUWBP7fB3+oUx5d/IIU4toOhgJqDZNoCp+oMnCxgfMuVlPBtGt+lvMEGHgRgnKn9gMyooYqQlksLEeqRt/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47047ad539c4c0b2f541b94ffa525262c268353038b3daddca81c3c04ca7e406","last_reissued_at":"2026-05-18T00:00:43.310640Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:43.310640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00982","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2o5pyGZsnOjXMrjOM5BZkA2CoayHYnKmOh5h6St7NvU9EmQqa10YClYX0srVRucUPgLcF6bUpqJnKTG3anZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:59:45.324425Z"},"content_sha256":"cf38cfcfe38e41f73d1ccf75a00be8324a193a645a6e01bab175252b9a833370","schema_version":"1.0","event_id":"sha256:cf38cfcfe38e41f73d1ccf75a00be8324a193a645a6e01bab175252b9a833370"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:I4CHVVJZYTALF5KBXFH7UUSSML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact R\\'enyi entropies of $D$-dimensional harmonic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"D. Puertas-Centeno, I. V. Toranzo, J. S. Dehesa","submitted_at":"2018-06-04T06:53:47Z","abstract_excerpt":"The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue \\textit{per se} and because these measures, which are functionals of the single-particle probability density of the systems, describe numerous fundamental and experimentally accessible physical quantities. However, it is a formidable task (not yet solved, except possibly for the ground and a few lowest-lying energetic states) even for the small bunch of elementary quantum potentials which are used to approximate the mean-field potential of the physical systems. Recently, the dominant term of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00982","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ix4HznZXcDD8bnJJkFfvlTtfa8Akrv5D36VO29Wu+R6Fe6KNentE5+nm0H87Qx2xHFYSEW7+/BGBIWZRQJV4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:59:45.325154Z"},"content_sha256":"1a6a4d9e16b6447e33fbe31624d1d9d03000c6835d220a6db77d8a2fd126323f","schema_version":"1.0","event_id":"sha256:1a6a4d9e16b6447e33fbe31624d1d9d03000c6835d220a6db77d8a2fd126323f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4CHVVJZYTALF5KBXFH7UUSSML/bundle.json","state_url":"https://pith.science/pith/I4CHVVJZYTALF5KBXFH7UUSSML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4CHVVJZYTALF5KBXFH7UUSSML/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T00:59:45Z","links":{"resolver":"https://pith.science/pith/I4CHVVJZYTALF5KBXFH7UUSSML","bundle":"https://pith.science/pith/I4CHVVJZYTALF5KBXFH7UUSSML/bundle.json","state":"https://pith.science/pith/I4CHVVJZYTALF5KBXFH7UUSSML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4CHVVJZYTALF5KBXFH7UUSSML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I4CHVVJZYTALF5KBXFH7UUSSML","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8ea0e0d4cbe64ea42eedf0e606dcfd1c3a8bef45263c7410e5e51c8fb6e7ef1c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-04T06:53:47Z","title_canon_sha256":"93ad8b867a765c92c898396d0e317959a725dc81cecc3640527fad8c6ab30750"},"schema_version":"1.0","source":{"id":"1806.00982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00982","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00982v1","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00982","created_at":"2026-05-18T00:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"I4CHVVJZYTAL","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"I4CHVVJZYTALF5KB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"I4CHVVJZ","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:1a6a4d9e16b6447e33fbe31624d1d9d03000c6835d220a6db77d8a2fd126323f","target":"graph","created_at":"2026-05-18T00:00:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The determination of the uncertainty measures of multidimensional quantum systems is a relevant issue \\textit{per se} and because these measures, which are functionals of the single-particle probability density of the systems, describe numerous fundamental and experimentally accessible physical quantities. However, it is a formidable task (not yet solved, except possibly for the ground and a few lowest-lying energetic states) even for the small bunch of elementary quantum potentials which are used to approximate the mean-field potential of the physical systems. Recently, the dominant term of t","authors_text":"D. Puertas-Centeno, I. V. Toranzo, J. S. Dehesa","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-04T06:53:47Z","title":"Exact R\\'enyi entropies of $D$-dimensional harmonic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00982","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cf38cfcfe38e41f73d1ccf75a00be8324a193a645a6e01bab175252b9a833370","target":"record","created_at":"2026-05-18T00:00:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8ea0e0d4cbe64ea42eedf0e606dcfd1c3a8bef45263c7410e5e51c8fb6e7ef1c","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-04T06:53:47Z","title_canon_sha256":"93ad8b867a765c92c898396d0e317959a725dc81cecc3640527fad8c6ab30750"},"schema_version":"1.0","source":{"id":"1806.00982","kind":"arxiv","version":1}},"canonical_sha256":"47047ad539c4c0b2f541b94ffa525262c268353038b3daddca81c3c04ca7e406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47047ad539c4c0b2f541b94ffa525262c268353038b3daddca81c3c04ca7e406","first_computed_at":"2026-05-18T00:00:43.310640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:43.310640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhEUWBP7fB3+oUx5d/IIU4toOhgJqDZNoCp+oMnCxgfMuVlPBtGt+lvMEGHgRgnKn9gMyooYqQlksLEeqRt/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:43.310994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf38cfcfe38e41f73d1ccf75a00be8324a193a645a6e01bab175252b9a833370","sha256:1a6a4d9e16b6447e33fbe31624d1d9d03000c6835d220a6db77d8a2fd126323f"],"state_sha256":"afb10d73c52d5079407c533140bc2966581aaeda452b736c3777328607d14a06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWHgygNlIv04uiIiAKGhLD2C+A+iFLfKs7qyz2df62rKmF2sWKGfBBoTUiZN0PSNCyPwDRmqtIxwbNSFgHm5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:59:45.329107Z","bundle_sha256":"6ed3402795f413add6840372c4100762f15eb364fb550286d73ab3f7fe3e514a"}}